AIR POLLUTION – MONITORING MODELLING AND HEALTH

Strategies for Estimation of Gas Mass Flux Rate Between Surface and the Atmosphere 269
& Ferrero, 1997). The diffusion coefficients, bij( xu , , t)
, for both forward and backward
integration is given by
b
ij
2
1/2
ij 2 i
Li
(16)
2
i
where ij is the Kronecker delta, and Li are velocity variance at each component and
the Lagrangian time scale (Degrazia et al., 2000), respectively. With the coordinates and the
mass of each particle, the concentration is computed (see below).
The inverse problem here is to identify the source term S(t). A source-receptor approach can
be employed for reducing the computer time, instead of running the direct model, Eq. (14),
for each iteration. This approach displays an explicit relation between the pollutant
concentration of the i-th receptor related the j-th sources:
where the matrix
C
N s
i MijSj
j1
(17)
M ij is the transition matrix, and each matrix entry given by
V V t N N
Mij
tNRi
, NSi , , j
Sj , Ri , Sj , Rij , ,
-forward model;
- backward model.
(18)
where V Ri , and V S,
j are the volume for the i-th receptor and j-th source, respectively; N S,
j
and N Ri , are the number of particle realised by the j-th source and i-th sensor, respectively;
N Ri ,, j and N Si ,, j are the number of particle released by the j-th source and detected by the
i-th receptor.
4. Determining gas flux between the ground and the atmosphere
For testing the procedure to estimate the emission rate procedure, it is considered the area
pollutant sources placed in a box volume, where the horizontal domain and vertical height
are given by: (1500 m 1000 m) 1000 m. There are two embedded regions R 1 and R 2 into
computational domain, with following horizontal domain (600 m 600 m) for each region,
and 1 m of height, and they are realising contaminants with two different emission rates.
Figure 1 shows the computational scenario in a two-dimensional projection ( xy): , the six
sensors are placed at 10 m height and spread horizontally with the coordinates presented in
Table 1. The domain is divided into sub-domains with 200 m 200 m 1 m. The emission
rates for each sub-domain ( S ) is as following:
A k
R 1 = S S S S S S = 10 gm -3 s -1 (Region-1)
A2 A3 A4 A7 A8 A9
R 2 = SA S 12 A S 13 A S 14 A S 17 A S
18 A = 20 gm -3 s -1 (Region-2)
19